Topic Seven: More Solving Problems Involving Addition and Subtraction
Pacing (Duration of Unit):
Desired Results
Transfer:
Standards for Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Established Goals: 2.OA.A.1-Represent and solve problems involving addition and subtraction.
1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Student I Can Statements:
I can write and solve problems using addition and subtraction.
I can use strategies to solve addition word problems. (within 100)
I can use strategies to solve subtraction word problems. (within 100)
Prerequisite Standards: 1.OA.A.2-Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
1.OA.B.3-Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known.(Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
1.OA.D.7-Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
1.OA.D.8-Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ?– 3, 6 + 6 =?.
Big Ideas: Operation Meanings and Relationships-There are multiple interpretations of addition, subtraction, multiplication, and division of rational numbers, and each operation is related to other operations.
Properties-For a given set of numbers there are relationships that are always true, called properties, and these are the rules that govern arithmetic and algebra.
Basic Facts and Algorithms-There is more than one algorithm for each of the operations with rational numbers. Some strategies for basic facts and most algorithms for operations with rational numbers, both mental math and paper and pencil, use equivalence to transform calculations into simpler ones.
Variables, Expressions, and Equations-Letters and symbols, called variables, can be used to stand for a number or any number from a particular set of numbers. Some mathematical and real-world situations can be represented using variables, operations, and numbers in expressions and equations.
Solving Equations and Inequalities-Rules of arithmetic and algebra can be used together with notions of equivalence to transform equations and inequalities so solutions can be found.
Practice, Processes, and Proficiencies-Mathematics content and processes can be applied to solve problems.
Essential Questions:
How can we solve word problems that use adding and subtracting?
Students will know...
You can write equations to model and solve word problems using a symbol, such as a question mark, to represent the unknown.
You can use drawings and equations to make sense of the words in word problems; and you can use strategies and algorithms to solve the problems and to check your work.
Sometimes a problem has an unstated, or hidden, question that you need to answer before you can find the final answer.
Sometimes the answer to one problem is needed to find the answer to another problem.
Good math thinkers know how to think about words and numbers to solve problems.
Vocabulary:
None
Studentswill be skilled at...
Model problems using equations with unknowns in any position.
Use drawings and equations to make sense of the words in problems.
Make sense of words in problems using drawings and equations.
Model and solve two-step problems using equations.
Solve two-step problems using different strategies.
Write and solve number stories using reasoning.
Assessment Evidence
Performance Assessment:
Other Evidence:
Learning Plan
Learning Activities:
7-1-Represent Addition and Subtraction Problems
7-2-Mixed Practice: Solve Addition and Subtraction Problems
7-3-Continue Practice with Addition and Subtraction Problems
Topic Seven: More Solving Problems Involving Addition and Subtraction
Pacing (Duration of Unit):Desired Results
Standards for Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
2.OA.A.1-Represent and solve problems involving addition and subtraction.
1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Student I Can Statements:
Prerequisite Standards:
1.OA.A.2-Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
1.OA.B.3-Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
1.OA.D.7-Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
1.OA.D.8-Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? – 3, 6 + 6 =?.
Operation Meanings and Relationships-There are multiple interpretations of addition, subtraction, multiplication, and division of rational numbers, and each operation is related to other operations.
Properties-For a given set of numbers there are relationships that are always true, called properties, and these are the rules that govern arithmetic and algebra.
Basic Facts and Algorithms-There is more than one algorithm for each of the operations with rational numbers. Some strategies for basic facts and most algorithms for operations with rational numbers, both mental math and paper and pencil, use equivalence to transform calculations into simpler ones.
Variables, Expressions, and Equations-Letters and symbols, called variables, can be used to stand for a number or any number from a particular set of numbers. Some mathematical and real-world situations can be represented using variables, operations, and numbers in expressions and equations.
Solving Equations and Inequalities-Rules of arithmetic and algebra can be used together with notions of equivalence to transform equations and inequalities so solutions can be found.
Practice, Processes, and Proficiencies-Mathematics content and processes can be applied to solve problems.
Vocabulary:
Assessment Evidence
Learning Plan
7-1-Represent Addition and Subtraction Problems
7-2-Mixed Practice: Solve Addition and Subtraction Problems
7-3-Continue Practice with Addition and Subtraction Problems
7-4-Solve Two-Step Problems
7-5-Continue to Solve Two-Step Problems
7-6-Math Practices and Problem Solving: Reasoning